________________

Numerical work and logical thinking are featured in the coach’s latest offerings.

________________

Close to a Quart

You are at a river and have two empty containers capable of holding exactly π (= 3.14159…) and e (= 2.7182818…) quarts of water.

How many transfers of water will it take you to get water in one container that is within 1% of a quart?

Math Party

At an annual party for a group of math professors, a couple tells a guest, “We have been married ten years. One year ago we gave Jones the sum and product of the ages of our three children, but Jones didn’t get their ages right. Smith missed the problem earlier tonight, having heard the current sum and product of our children’s ages.” Assume all children’s ages are whole numbers less than ten.

Solutions to week 137

In Room for One More, for n = 164, there is just enough room for 329 circles. For End Points, color the two ends of all diameters with different colors. There are an infinite number of ways to do this. Since the hypotenuse of any inscribed right triangle is always a diameter, those two vertices will have different colors.

Room for One More answer explained:
The circles are packed as shown below with spacing between circles as indicated. There are 7 circles on each end, with 105 sets of 3 circles in the middle. The smallest rectangle found so far containing 329 circles has 13 circles on each side, with 101 sets of 3 circles in the middle, and is 2 by 163.9973967…